What is the integral from-pi/2 to pi/2 of (cos(x)-1) ?

The integral from-pi/2 to pi/2 of (cos(x)-1) is 2-pi

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integral from-pi/2 to pi/2 of (cos(x)-1)

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 1) d x

2 - π

Decimal Notation

- 1.14159 \dots

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x - \int_{- \frac{π}{2}}^{\frac{π}{2}} 1 d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x = 2

\int_{- \frac{π}{2}}^{\frac{π}{2}} 1 d x = π

= 2 - π

\int_{0}^{\frac{π}{4}} 2 cos (x) d x

\int_{0}^{x} tan (t) d t

\int_{0}^{3} 8 x d x

\int_{0}^{\frac{π}{4}} cos^{3} (x) d x

\int_{0}^{2} 3^{x} (1 - 2^{x}) d x

What is the integral from-pi/2 to pi/2 of (cos(x)-1) ?
The integral from-pi/2 to pi/2 of (cos(x)-1) is 2-pi